Question: Simplify the following expression: $y = \dfrac{-2q^2 + 26q - 60}{q - 10} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ y =\dfrac{-2(q^2 - 13q + 30)}{q - 10} $ Then we factor the remaining polynomial: $q^2 {-13}q + {30} $ ${-10} {-3} = {-13}$ ${-10} \times {-3} = {30}$ $ (q {-10}) (q {-3}) $ This gives us a factored expression: $\dfrac{-2(q {-10}) (q {-3})}{q - 10}$ We can divide the numerator and denominator by $(q + 10)$ on condition that $q \neq 10$ Therefore $y = -2(q - 3); q \neq 10$